What they had in mind was ensuring that the government and its minions didn't have sole access to the means of coercive force.

Exactly the wording I was looking for. Our own Marko Kloos wrote an excellent essay on the matter called Why the Gun Is Civilization that is well worth reading on the matter.

Quote:

Human beings only have two ways to deal with one another: reason and force. If you want me to do something for you, you have a choice of either convincing me via argument, or force me to do your bidding under threat of force. Every human interaction falls into one of those two categories, without exception. Reason or force, that’s it.

In a truly moral and civilized society, people exclusively interact through persuasion. Force has no place as a valid method of social interaction, and the only thing that removes force from the menu is the personal firearm, as paradoxical as it may sound to some.

This applies not only to interactions between individuals, but to interactions between individuals and the state.

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Sometimes it’s nice not to destroy the world for a change.
--Randall Munroe